Non-resonant secular dynamics of trans-Neptunian objects perturbed by a distant super-Earth |
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| Authors: | Melaine Saillenfest Marc Fouchard Giacomo Tommei Giovanni B Valsecchi |
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| Institution: | 1.IMCCE,Paris,France;2.Dipartimento di Matematica,Università di Pisa,Pisa,Italy;3.PSL Research University, CNRS, Sorbonne Universités, UPMC Université Paris 06, LAL, Université de Lille,Paris/Lille,France;4.IAPS-INAF,Rome,Italy;5.IFAC-CNR,Sesto Fiorentino,Italy |
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| Abstract: | We use a secular model to describe the non-resonant dynamics of trans-Neptunian objects in the presence of an external ten-Earth-mass perturber. The secular dynamics is analogous to an “eccentric Kozai mechanism” but with both an inner component (the four giant planets) and an outer one (the eccentric distant perturber). By the means of Poincaré sections, the cases of a non-inclined or inclined outer planet are successively studied, making the connection with previous works. In the inclined case, the problem is reduced to two degrees of freedom by assuming a non-precessing argument of perihelion for the perturbing body. The size of the perturbation is typically ruled by the semi-major axis of the small body: we show that the classic integrable picture is still valid below about 70 AU, but it is progressively destroyed when we get closer to the external perturber. In particular, for \(a>150\) AU, large-amplitude orbital flips become possible, and for \(a>200\) AU, the Kozai libration islands at \(\omega =\pi /2\) and \(3\pi /2\) are totally submerged by the chaotic sea. Numerous resonance relations are highlighted. The most large and persistent ones are associated with apsidal alignments or anti-alignments with the orbit of the distant perturber. |
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